WASHINGTON — Republican governors are often seen as innovative policymakers and potential presidential candidates, but a few are struggling with political or ethical problems that might crimp their ambitions.

Two governors eyeing possible White House bids — Bob McDonnell of Virginia and Bobby Jindal of Louisiana — suddenly find themselves fending off critics and trying to shore up legacies they hope will withstand national scrutiny. Other high-profile governors run the gamut from maintaining solid popularity to being in danger of losing re-election next year.

Governorships can be springboards to the White House, as Ronald Reagan, Bill Clinton, George W. Bush and others have shown. But the high visibility also can lead to painful falls.

McDonnell, who built an image as a competent problem-solver, confronted questions Tuesday about an FBI inquiry into gifts he accepted from a wealthy Virginia businessman. And Jindal, even in a Republican-dominated state, had to pull back his ambitious plan to replace Louisiana's corporate and personal income taxes with higher sales taxes. His popularity has sagged lately.

The 2016 presidential election is far away, of course, and the GOP has plenty of possible contenders. They include current and former governors, such as Chris Christie of New Jersey and Jeb Bush of Florida.

Still, McDonnell's and Jindal's struggles — combined with those of Republican governors in Pennsylvania, Florida, South Carolina and elsewhere — prove that governorships can be far from ideal incubators of political ideas and national ambitions.

"It's a double-edge sword, being chief executive," said John Ullyot, a Republican strategist and former Senate aide from Virginia. Effective governors, he said, can implement agendas and build reputations for bipartisanship, as Christie has sometimes done in New Jersey.

"But if something goes wrong in your state," Ullyot said, "there's no one to blame but you."

Starting with McDonnell and Christie in 2009, and followed by an impressive class the following year, Republicans won gubernatorial races in numerous states carried by President Barack Obama in 2008 and 2012. They included Ohio, Pennsylvania, Michigan, Wisconsin, Florida and New Mexico.

Politically, the timing was ideal. GOP control of these battleground states enabled Republicans to dominate the once-a-decade redrawing of congressional districts after the 2010 census. It's one reason Republicans hold a 31-seat House majority even though Americans cast a million more votes last November for Democratic House candidates than for Republicans.

Some of these new GOP governors — mostly notably John Kasich of Ohio and Scott Walker of Wisconsin — pushed conservative agendas so fast and fiercely that the public backlash forced them to regroup and proceed more diplomatically.

Republican Govs. Tom Corbett of Pennsylvania and Rick Scott of Florida, who have lower national profiles, are among those still struggling to rebound from early problems.

McDonnell's and Jindal's woes draw notice beyond their states because they are among the half-dozen or so most-discussed Republicans in early political chatter about 2016. Democrats have ambitious governors, too, including Maryland's Martin O'Malley and New York's Andrew Cuomo. But Hillary Rodham Clinton and Vice President Joe Biden tend to dominate early Democratic talk about Obama's possible successor.

In Virginia, McDonnell had enjoyed comfortable approval ratings and was seen as a conservative pragmatist unafraid to compromise. Last winter, he achieved a landmark overhaul of the state's failing system for funding road construction and addressing acute gridlock in the Washington suburbs and the Norfolk region.

That image was rocked by Monday's news that the FBI is examining ties McDonnell and his wife, Maureen, have with a Virginia-based food supplements maker that's the subject of a federal securities probe and two shareholder lawsuits.

McDonnell told WTOP radio that his administration never gave special treatment to Star Scientific Inc. or its CEO, Jonnie Williams, who had given McDonnell more than $100,000 in political contributions and spent thousands of dollars more on personal gifts to McDonnell and his family.

Virginia law did not require the governor to disclose the $15,000 that Williams gave McDonnell's daughter Cailin for her wedding. But in his radio appearance Tuesday, McDonnell acknowledged the political sensitivity of the matter.

"I think, obviously, from the attention it has gotten, it has certainly now been disclosed," he said. He said it was hard to say whether he would ask his daughter to reject the gift if given a chance to do it over. "It's caused a fair amount of pain for me personally," McDonnell said. "I'm a governor, but I'm also a dad and I love my daughter very much."

In Louisiana, polls and anecdotal evidence suggest many people have grown tired of Jindal's national travels, state government layoffs and budget cuts, especially to health care and higher education. His sweeping tax plan drew wide criticism.

It marked a setback for the fast-talking Rhodes scholar, who has urged the GOP to stop being "the stupid party" that's out of step on key social matters.

In the past 50 years, more governors and vice presidents have been elected president than have sitting senators, although a few senators almost always try. Republican senators weighing possible presidential bids in 2016 include Rand Paul of Kentucky and Marco Rubio of Florida.

Republican Mitt Romney and Democrat Michael Dukakis are among the incumbent or former governors who won their party's nomination but failed to win the White House. Four of the last six presidents, however, were governors.